If tan−1⁡1+x2−1−x21+x2+1−x2=α, then x2 =

Since, tan−1⁡1+x2−1−x21+x2+1−x2=α⇒1+x2−1−x21+x2+1−x2=tan⁡α1Using componendo and dividendo, we get21+x221−x2=1+tan⁡α1−tan⁡α=tan⁡π4+α⇒1+x21−x2=tan2⁡π4+α1Again using componendo and dividendo, we have1+x2−1−x21+x2+1−x2=tan2⁡(π/4+α)−1tan2⁡(π/4+α)+1⇒x2=−cos⁡π2+2α=sin⁡2α